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			<span class="lang">
<span class="lang-ja">
<p>配点 : <var>400</var> 点</p>

<div class="part">
<section>
<h3>問題文</h3><p>高橋君と青木君が選挙で戦っています。<br />
選挙区は <var>N</var> 個あります。<var>i</var> 番目の選挙区には <var>X_i + Y_i</var> 人の有権者がいて、そのうち <var>X_i</var> 人が高橋派、<var>Y_i</var> 人が青木派です。(<var>X_i + Y_i</var> はすべて奇数です)<br />
それぞれの区では、多数派がその区の <var>Z_i</var> 議席を全て獲得します。そして、<var>N</var> 個の選挙区全体として過半数の議席を獲得した方が選挙に勝利します。(<var>\displaystyle \sum_{i=1}^N Z_i</var> は奇数です)<br />
高橋君が選挙で勝利するには最低で何人を青木派から高橋派に鞍替えさせる必要がありますか？</p>
</section>
</div>

<div class="part">
<section>
<h3>制約</h3><ul>
<li><var>1 \leq N \leq 100</var></li>
<li><var>0 \leq X_i, Y_i \leq 10^9</var></li>
<li><var>X_i + Y_i</var> は奇数</li>
<li><var>1 \leq Z_i</var></li>
<li><var>\displaystyle \sum_{i=1}^N Z_i \leq 10^5</var></li>
<li><var>\displaystyle \sum_{i=1}^N Z_i</var> は奇数</li>
</ul>
</section>
</div>

<hr />
<div class="io-style">
<div class="part">
<section>
<h3>入力</h3><p>入力は以下の形式で標準入力から与えられる。</p>
<pre><var>N</var>
<var>X_1</var> <var>Y_1</var> <var>Z_1</var>
<var>X_2</var> <var>Y_2</var> <var>Z_2</var>
<var>\vdots</var>
<var>X_N</var> <var>Y_N</var> <var>Z_N</var>
</pre>

</section>
</div>

<div class="part">
<section>
<h3>出力</h3><p>答えを出力せよ。</p>
</section>
</div>
</div>

<hr />
<div class="part">
<section>
<h3>入力例 1</h3><pre>1
3 8 1
</pre>

</section>
</div>

<div class="part">
<section>
<h3>出力例 1</h3><pre>3
</pre>

<p>選挙区が <var>1</var> 個しかないので、<var>1</var> 番目の選挙区で議席を獲得した人が選挙に勝利します。<br />
<var>1</var> 番目の選挙区の青木派 <var>3</var> 人を高橋派に鞍替えさせると、<var>1</var> 番目の選挙区にいる有権者のうち高橋派は <var>6</var> 人、青木派は <var>5</var> 人になり、高橋君は議席を獲得できます。</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>入力例 2</h3><pre>2
3 6 2
1 8 5
</pre>

</section>
</div>

<div class="part">
<section>
<h3>出力例 2</h3><pre>4
</pre>

<p><var>1</var> 番目の選挙区の議席数よりも <var>2</var> 番目の選挙区の議席数の方が多いため、高橋君が選挙に勝つには <var>2</var> 番目の選挙区で高橋派を多数派にする必要があります。<br />
<var>2</var> 番目の選挙区の青木派の <var>4</var> 人を鞍替えさせると高橋君は <var>5</var> 議席を獲得できます。このとき青木君の獲得する議席は <var>2</var> 議席なので、高橋君は選挙に勝利できます。</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>入力例 3</h3><pre>3
3 4 2
1 2 3
7 2 6
</pre>

</section>
</div>

<div class="part">
<section>
<h3>出力例 3</h3><pre>0
</pre>

<p>青木派から高橋派に鞍替えする人が <var>0</var> 人でも高橋君が選挙で勝つ場合は <var>0</var> 人が答えになります。</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>入力例 4</h3><pre>10
1878 2089 16
1982 1769 13
2148 1601 14
2189 2362 15
2268 2279 16
2394 2841 18
2926 2971 20
3091 2146 20
3878 4685 38
4504 4617 29
</pre>

</section>
</div>

<div class="part">
<section>
<h3>出力例 4</h3><pre>86
</pre></section>
</div>
</span>
<span class="lang-en">
<p>Score : <var>400</var> points</p>

<div class="part">
<section>
<h3>Problem Statement</h3><p>Takahashi and Aoki are competing in an election.<br />
There are <var>N</var> electoral districts. The <var>i</var>-th district has <var>X_i + Y_i</var> voters, of which <var>X_i</var> are for Takahashi and <var>Y_i</var> are for Aoki. (<var>X_i + Y_i</var> is always an odd number.)<br />
In each district, the majority party wins all <var>Z_i</var> seats in that district. Then, whoever wins the majority of seats in the <var>N</var> districts as a whole wins the election. (<var>\displaystyle \sum_{i=1}^N Z_i</var> is odd.)<br />
At least how many voters must switch from Aoki to Takahashi for Takahashi to win the election?</p>
</section>
</div>

<div class="part">
<section>
<h3>Constraints</h3><ul>
<li><var>1 \leq N \leq 100</var></li>
<li><var>0 \leq X_i, Y_i \leq 10^9</var></li>
<li><var>X_i + Y_i</var> is odd.</li>
<li><var>1 \leq Z_i</var></li>
<li><var>\displaystyle \sum_{i=1}^N Z_i \leq 10^5</var></li>
<li><var>\displaystyle \sum_{i=1}^N Z_i</var> is odd.</li>
</ul>
</section>
</div>

<hr />
<div class="io-style">
<div class="part">
<section>
<h3>Input</h3><p>The input is given from Standard Input in the following format:</p>
<pre><var>N</var>
<var>X_1</var> <var>Y_1</var> <var>Z_1</var>
<var>X_2</var> <var>Y_2</var> <var>Z_2</var>
<var>\vdots</var>
<var>X_N</var> <var>Y_N</var> <var>Z_N</var>
</pre>

</section>
</div>

<div class="part">
<section>
<h3>Output</h3><p>Print the answer.</p>
</section>
</div>
</div>

<hr />
<div class="part">
<section>
<h3>Sample Input 1</h3><pre>1
3 8 1
</pre>

</section>
</div>

<div class="part">
<section>
<h3>Sample Output 1</h3><pre>3
</pre>

<p>Since there is only one district, whoever wins the seat in that district wins the election.<br />
If three voters for Aoki in the district switch to Takahashi, there will be six voters for Takahashi and five for Aoki, and Takahashi will win the seat.</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>Sample Input 2</h3><pre>2
3 6 2
1 8 5
</pre>

</section>
</div>

<div class="part">
<section>
<h3>Sample Output 2</h3><pre>4
</pre>

<p>Since there are more seats in the second district than in the first district, Takahashi must win a majority in the second district to win the election.<br />
If four voters for Aoki in the second district switch sides, Takahashi will win five seats. In this case, Aoki will win two seats, so Takahashi will win the election.</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>Sample Input 3</h3><pre>3
3 4 2
1 2 3
7 2 6
</pre>

</section>
</div>

<div class="part">
<section>
<h3>Sample Output 3</h3><pre>0
</pre>

<p>If Takahashi will win the election even if zero voters switch sides, the answer is <var>0</var>.</p>
</section>
</div>

<hr />
<div class="part">
<section>
<h3>Sample Input 4</h3><pre>10
1878 2089 16
1982 1769 13
2148 1601 14
2189 2362 15
2268 2279 16
2394 2841 18
2926 2971 20
3091 2146 20
3878 4685 38
4504 4617 29
</pre>

</section>
</div>

<div class="part">
<section>
<h3>Sample Output 4</h3><pre>86
</pre></section>
</div>
</span>
</span>

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